Question

What is the approximate 95% prediction interval for the dependent variable when the independent variable value is 20, assuming the fitted regression line is: Y = 1.50 + 6.0(X). Assume the sample size is 20 and the standard error of the regression (SEE) is 1.2. You should use the "rule of thumb" used in class here.

Answer 1

Answer:

Step-by-step explanation:

95% prediction interval for the dependent variable when the independent variable value is 20,

assuming the fitted regression line is: Y = 1.50 + 6.0(X).

Assume the sample size is 20

Y = 1.50 + 6.0(X)

sample X = 20

here predicted value = 1.5+6*20

= 121.5

therefore 95% prediction interval for the dependent variable

the standard error of the regression (SEE) is 1.2.

$=121.5 \pm 2*1.2\\\\=121.1+2*1.2\\\\=121.1+2.4\\\\=123.9\ \texttt {and} \\\\=121.1-2*1.2\\\\=121.1-2.4\\\\=119.1 \\\\(119.10 \ \text {to}\ 123.90)$